In chemistry, the Möbius–Hückel treatment is a methodology used to predict whether a reaction is allowed or forbidden. It is often used along with the Woodward–Hoffmann approach. The description in this article uses the plus-minus sign notation for parity as shorthand while proceeding around a cycle of orbitals in a molecule or system, while the Woodward–Hoffmann methodology uses a large number of rules with the same consequences. Introduction One year following the Woodward–Hoffmann and Longuet-Higgins–Abrahmson publications, it was noted by Zimmerman that both transition states and stable molecules sometimes involved a Möbius array of basis orbitals. The Möbius–Hückel treatment provides an alternative to the Woodward–Hoffmann one. In contrast to the Woodward–Hoffmann approach the Möbius–Hückel treatment is not dependent on symmetry and only requires counting the number of plus-minus sign inversions in proceeding around the cyclic array of orbitals. Where one has zero or an even number of sign inversions there is a Hückel array. Where an odd-number of sign inversions is found a Möbius array is determined to be present. Thus the approach goes beyond the geometric consideration of Edgar Heilbronner. In any case, symmetry may be present or may not. Edgar Heilbronner had described twisted annulenes which had Möbius topology, but in including the twist of these systems, he concluded that Möbius systems could never be lower in energy than the Hückel counterparts. In contrast, the Möbius–Hückel concept considers systems with an equal twist for Hückel and Möbius systems. The theory and concept For Möbius Systems there is an odd number of plus-minus sign inversions in the basis set in proceeding around the cycle. A circle mnemonic was advanced which provides the MO energies of the system; this was the counterpart of the Frost–Musulin mnemonic for ordinary Hückel systems. It was concluded that 4n electrons is the preferred number for Möbius moieties in contrast to the common 4n + 2 electrons for Hückel systems. The Möbius–Hückel circle mnemonic To determine the energy levels, the polygon corresponding to the cyclic annulene is desired is inscribed in the circle of radius 2β and centered at α (the energy of an isolated p orbital). The y-coordinate of the vertices of the polygon are the simple Hückel theory orbital energies. For systems with Hückel topology, the vertex is positioned at the circle bottom as suggested by Frost; for systems with Möbius topology, a polygon side is positioned at the circle bottom. In other